Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

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63 views

How did the author solve this integral?

I have the following spherical density distribution: $\rho(x, z) = \frac{1}{\sqrt{x^2 + z^2}\left(1+\sqrt{x^2+z^2}\right)^2}$ which I have broken into a "line of sight" dimension $z$ and a &...
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33 views

Triple series with WolframAlpha where the series are interdependent

How can be written a triple series with WolframAlpha where the series are interdependent like, for instance, the following ones? $$\sum_{i=1}^{n-2} \sum_{j=i+1}^{n-1} \sum_{k=j+1}^{n} \min\{j-i,k-j\}~....
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19 views

Double series with WolframAlpha where the series are interdependent

How can be written a double series with WolframAlpha where the series are interdependent like, for instance, the following ones? $$\sum_{j=1}^i \sum_{i=2}^n (i^2-j)$$ (I don't get, as expected, a ...
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1answer
58 views

What's going on with this Wolfram Alpha matrix multiplication?

I was computing the matrix exponential of $$X = \begin{pmatrix} 1 & -1 & 0 \\ -1 & 2 & -1 \\ 0 & -1 & 1 \end{pmatrix}$$ by diagonalization. Wolfram Alpha and Symbolab both ...
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23 views

How can I solve this set of complex integral equations on Wolfram/Mathematica?

I need to evaluate the complex line integral in the following equation: $$f(z) = \int_0^z \zeta^{-3/4}(\zeta-a)^{-1/2}(\zeta-1)^{-1/2}d\zeta,$$ where $a$ is determined from the equation: $$\int_0^a=-...
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1answer
56 views

How can I evaluate this complex integral equation on Wolfram?

I need to evaluate the complex line integrals in the following equation: $$g(z)=\frac{\int_0^z\zeta^{-5/6}(\zeta-1)^{-1/2}d\zeta}{\int_0^1\zeta^{-5/6}(\zeta-1)^{-1/2}d\zeta}.$$ Can someone advise me ...
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25 views

Wolfram Alpha for Integer Programming

I am new to Wolfram Alpha. The following command gives me real number solutions: max 8*p+20*q, p+q ≤11, 3*p+2*q≤30, p+3*q≤28, p≥0, q≥0 The solution is p = 5/2 and ...
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14 views

How to label different plots on one graph

I need to sign each plot separately, but I don’t know how to do it. PlotLabel signs all of them above the y axis
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20 views

how to use implicit differentiation using Wolfram alpha. two dependent variables

Im stuck trying to feed the formula into Wolfram alpha, I gotta solve for $\frac{d}{dt}{x^2y^2}=16$
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1answer
58 views

I found an unusual (at least for me) answer in Wolfram Alpha I don't understand

Sorry in advance, is my first question and i found something weird in wolfram The problem: Given a function f, and a chain of links with lengths (h0, h1, h2...), calculate the points where every ...
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1answer
76 views

Should I waste my time with wolfram alpha to solve such problem like $x^3+y^3+z^3=390$?

I'm sorry to ask this question probably it is not suitable here. However I read some papers in number theory related to the solution of $x^3+y^3+z^3=n$ for some known solved problem about ...
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1answer
26 views

Specify parameters Wolfram Alpha

Hopefully, this kind of question is ok, have seen a couple of other WA-queries that hasn't been downvoted. Apologies if not. I want to minimize say $f(x)=ax^2+bx+c$. Wolfram Alpha gives me an ...
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3answers
64 views

How do I calculate the sine integral for a specific input?

I need to solve an equation containing the Sine Integral $\mathrm{Si}\left(\frac{2 k \pi}{x}\right)$ in mathjs which doesn't have the $\mathrm{Si}$ function. Is there another way to represent this? ...
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1answer
19 views

Series expression by using Puiseux series

I wanna express this series $$\sqrt{1}+\sqrt{2}+\sqrt{3}+\sqrt{4}+...+\sqrt{n}$$ as Puiseux series. According to "Wolfram Alpha", it says $$\frac{2n^{3/2}}{3}+\frac{\sqrt{n}}{2}+\zeta(-\frac{1}{2})+\...
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0answers
80 views

What are the mathematical steps used to get this $42=(-80538738812075974)³ + 80435758145817515³ + 12602123297335631³$?

I have accrossed this representation in cubic sum $42=(-80538738812075974)³ + 80435758145817515³ + 12602123297335631³$ at this website but am confused how mathematicains proved this , Now Is this ...
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1answer
72 views

Why does $\tan\left(\frac{1}{x}\right)$ look different to what I expect it should look like on WolframAlpha as x approaches 0?

https://www.wolframalpha.com/input/?i=tan%281%2Fx%29%2C+-0.01+%3C+x+%3C+0.01 $$$$ https://www.wolframalpha.com/input/?i=tan%281%2Fx%29%2C+-0.001+%3C+x+%3C+0.001 $$$$ For larger intervals of x, ...
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62 views

Why does Mathematica / Wolfram Alpha gives 2 different answers for these 2 queries?

I was assigned to find the integral of this expression: $$ \int\frac{-5x^3+3x^\frac{3}{2}-2x^2-5x + \frac{3}{\sqrt x}}{x^2+1}\mathrm{d}x$$ I did: $$ = \int\frac{-5x(x^2 + 1)}{x^2+1} \mathrm{d}x + \...
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1answer
51 views

Is it mathematically valid to take the limit of an **equation** as opposed to an expression?

Wolfram Alpha seems to think it's okay to write this: $$\lim_{n \to \infty} (n=\frac{n^2}{n})=True$$ I understand what is meant, and also why it returns True, but is this a mathematically valid ...
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1answer
55 views

Wolfram Alpha is doing something I don't understand, please help

I am using Newton Raphson method to obtain the velocity of a chemical reaction, and I needed to derive the next equation:$$\frac{d}{dk}\left(\left(\frac{0.35}{k}\right)^{\frac{k}{k-0.35}}\right)= -0....
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2answers
58 views

Find $a, b, c$ such that element $x=a\alpha^2+b\alpha+c \in \mathbb{Q}[x]/\langle x^3+x+11 \rangle$

I'm trying to generate a fundamental unit of the number field $K=\mathbb{Q}(\alpha)$, where $\alpha^3+\alpha+11$. I found a non-trivial unit and I need to find $a,b,c\in\Bbb{Q}$ such that $$\frac{(-...
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1answer
89 views

Help with gnarly integral from fluid mechanics

I'm working on a 2D fluid simulator and a particularly gnarly integral came up. First, I have two functions in polar coordinates which look like: $$F(\theta) = cos(2\theta+\psi)$$ $$ G(\theta) = \...
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1answer
55 views

What is this method of solving called and why does it work? (From WA)

Wolfram Alpha uses a scary-looking algebraic method to solve $x^{3}-x-1=0$ that I've never encountered before. It seems that every other online algebra calculator uses numerical methods, such as the ...
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3answers
167 views

Computer tools to solve linear system of equations with singular matrix

According to the theory I've read, if $A$ is singular, the equation $A\vec{x}=\vec{b}$ will have either zero or infinitely many solutions. I tried solving this equation for: $$A=\begin{bmatrix} 4 &...
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2answers
37 views

Find the leading digit(s) of a factorial

What are the better methods (algorithms) to computing the first number (or few leading numbers) of a large factorial. Wolfram alpha seems pretty fast and handles large numbers. Is it accurate? Does ...
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50 views

How to calculate the area of a polar curve in Wolfram Alpha?

I know I can use plot polar r = cos(3theta), theta from pi/6 to -pi/6 to plot the polar curve of a equation, but I would like to check if my math is correct when calculating the area inside the curve. ...
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4answers
65 views

How to plot the polar equation theta = pi/6 on wolframalpha

I need to plot the polar equation theta = pi/6 My question has two parts. 1) Is it a line? I'm pretty sure it is, since the angle theta in the polar equation is a constant, but since I was not ...
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1answer
40 views

intersection of numbers on wolfram [closed]

After evaluations of the Riemann Hypothesis, with reflective thoughts over a year as to how to solve it, a formula that is very close has been found, if not distinctly the act of the original proof, ...
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2answers
41 views

Iterative Equations in Wolfram Alpha

I am trying to solve an iterated equation, but it is quite messy and I am having trouble. Here are my equations: $$ \mu_{t+1} = \frac{h_t \mu_t + h_\epsilon Z_t}{h_t + h_\epsilon} $$ and $$h_{t+...
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1answer
42 views

What is Wolfram doing?

According to Wolfram Alpha, $$\frac{T\cos^2(\pi m)}{\pi-2\pi m} + \frac{T\cos^2(\pi m)}{2\pi m + \pi}$$ has an alternate form $$\frac{2T\cos^2(\pi m)}{\pi-4\pi m^2}$$ and I am not able to see the ...
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2answers
67 views

What is Wolfram Alpha doing here in solving $x^3=8$? [closed]

I have no problem finding the three solution to the very simple cubic equation $x^3=8$. But I can't understand what Wolfram Alpha is trying to convey in the part underlined in blue.
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52 views

Using wolfram alpha to solve IVP

How can wolfram alpha be used to find the solution to an IVP, if the IVP has non integers in the condition For example, The half in the function was changed to multiply outside(it does this for any ...
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1answer
63 views

Sum of product result given by wolfram: $\sum_{k=1}^\infty\prod_{i=1}^k\frac{3i-1}{4i}=2(2)^\frac{1}{3}-1$

So according to Wolfram Alpha, the following result holds: $$\sum_{k=1}^\infty\prod_{i=1}^k\frac{3i-1}{4i}=2(2)^\frac{1}{3}-1$$ Could someone explain to me how Wolfram Alpha gets this or how to ...
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2answers
52 views

Show that: $\lim_{n\rightarrow\infty}e^{\frac{\log x}{\log\log xn-\log\log n}-\log\left(n\right)}=\sqrt{x}$.

I want to show that: $$\lim_{n\rightarrow\infty}e^{\frac{\log x}{\log\log xn-\log\log n}-\log\left(n\right)}=\sqrt{x}$$ I looked it up on Wolfram Alpha, and it says: $$\lim_{n\rightarrow\infty}e^{\...
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1answer
65 views

Evaluating an improper integral with the help of WA

Let $$I = \int_0^\infty\frac{x\sin 3x}{(x^2+16)^2}$$ Find $I$ using complex integration. My try: We should consider $$f(z) = \frac{ze^{3iz}}{(z^2+16)^2}$$ Using WA, I found that $\operatorname{res}_{...
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24 views

How do I verify the correctness of long derivations?

Given a constant vector $\mathbf{d}$ and the unit vector \begin{align*} \mathbf{n}(\theta, \phi) = \begin{bmatrix} \cos\theta\sin\phi\\[0.001cm] \sin\theta\sin\phi\\[0.001cm] \cos\phi \end{...
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2answers
51 views

Determine if function $f(x)=\ln \left ( \frac{x+1}{x-1} \right )$ is odd or even.

Determine if function $f(x)=\ln \left ( \frac{x+1}{x-1} \right )$ is odd or even. My solution: $$ \begin{align} f(-x)&=\ln\left ( \frac{-x+1}{-x-1} \right )\\ &=\ln \left ( \frac{-(x-1)}{-(x+...
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1answer
58 views

Explanation of the precision and the accuracy used by Wolfram Mathematica when performing arithmetic operations on floating point numbers

The numerical value for the precision in mathematica is given out by $MachinePrecision, and this is also the number of relevant digits showed in the output console ...
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1answer
43 views

How to tell Wolfram Alpha to evaluate only odd/even numbers [closed]

Similarly to this question and with notation much like discussed here is there any way to tell Wolfram Alpha that I want a function evaluated only at even or odd integers? My goal is to (manually) ...
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0answers
22 views

Plot phase portrait of three-variable system of kinetic equations

I have a system of three kinetic equations with three variables $x,y,z$, i.e. : $$\dfrac{dx}{dt}=f(x,y,z)$$ $$\dfrac{dy}{dt}=g(x,y,z)$$ $$\dfrac{dz}{dt}=p(x,y,z)$$ In WolframAlpha you can just put ...
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1answer
106 views

A solution for the integral $\int \frac{\sqrt[3]{x} }{\sqrt[3]{x^2} -\sqrt{x} } dx $ and WA's “invalid input”.

Problem: $$\displaystyle \int \frac{\sqrt[3]{x}}{\sqrt[3]{x^2} -\sqrt{x} } dx$$ My attempts: $$\displaystyle \int \frac{\sqrt[3]{x}}{\sqrt[3]{x^2} -\sqrt{x} } dx={\displaystyle\int} \dfrac{1}{6x^\...
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0answers
50 views

Wolfram Alpha equation I couldn't find anywhere

I was just playing around with Wolfram Alpha and n-th derivatives of functions, and I found this....n-th derivative of W(x) equation As you can see, there are some weird functions. I found most of ...
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1answer
53 views

Wolfram-Alpha closed form of product of Gamma function

Wolfram-Alpha recognizes this closed form \begin{align} \prod_{k=1}^{n-1}\sin(\pi k/n) &= 2^{1-n}\,n \end{align} just fine but fails on this one, despite that this expression also has a known ...
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1answer
33 views

log 0xffff base 0xff is not 2

I tested on wolfram alpha and rust language and the log(0xff, 0xffff), is not 2 but 0xff power 2 equals 0xffff. The result is 2.00141... Why does this happen? I have a 4 byte number and I want to get ...
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1answer
20 views

Solving for $y_\infty$

Solving the following equation for $y_\infty$ took hours with me, all ways were not feasible. I tried WolframAlpha, it says the variable is not present in the equation. $x_1,y_1,x_2,y_2,x_3,$ and $...
1
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1answer
23 views

Wolfram Alpha: How to evaluate the difference of a function at two points

I'm just using the website and not the programming language or anything like that. I want to type in: evaluate x from 2 to 5 and get ...
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3answers
180 views

Why can't Wolfram Alpha compute this integral?

$$\int_0^\infty \int_0^\infty \lambda_1\lambda_2 \mid{x - y} \mid e^{-\lambda_1x - \lambda_2y} dy dx$$ $$= \int_0^{\infty} e^{-\lambda_1x}\bigg[ \int_0^x(x - y)e^{-\lambda_2y}dy + \int_x^\infty(y - x)...
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2answers
170 views

Wrong result in Wolfram Alpha on graph

I'm learning to code in Python, so I tried to find roots and draw a graph of a function $-(16x^2-24x+5)e^{-x}$ 1 Result i got in Python using the mat.plotlib library is this The problem is that ...
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3answers
35 views

Maximum and minimum of $f(x)= \sin x(1- \cos x)$ at $[0,2\pi] \to [-2,2|$

Let $f:[0,2\pi] \to [-2,2|$ with $$f(x)= \sin x(1- \cos x)$$ Using WolframAlpha I checked that the maximum is at $2\pi n + (2\pi/3)$ and the minimum at $2\pi n - (2\pi/3)$ But how can I get to ...
2
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1answer
157 views

Is x^1/3 the same as cube root(x)?

I needed to evaluate the surjectivity of cuberoot(x) and used Wolfram-Alpha for that. To my surprise, cuberoot(x) is different ...
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3answers
214 views

Evaluation of complete elliptic integral of second kind

I am currently working to try and solve the integral: $$\int_{0}^{\frac{\pi}{2}} \sqrt{1-a^2\cos(x)^2} = \sqrt{1-a^2} \; E\left ( 1+\frac{1}{-1+a^2} \right )$$ where $E(m)$ is the complete elliptic ...

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